A GENERAL SELF-SIMILAR MODEL AND THE P-D DIAGRAM OF EXTRAGALACTIC RADIO SOURCES

The great majority of analytical models for extragalactic radio sources suppose self-similarity and can be classified into three types. We have developed a model that represents a generalization of most models found in the literature and show that these three types are particular cases. The model assumes that the area of the head of the jet varies with the jet size according to a power law and the jet luminosity is a function of time. As is usually done, the basic hypothesis is that there is an equilibrium between the pressure exerted both by the head of the jet and the cocoon walls and the ram pressure of the ambient medium. The equilibrium equations and energy conservation equation allow us to express the size and width of the source and the pressure in the cocoon as a power law and find the respective exponents. Once we find these exponents, we can determine the initial values of the source size, the cocoon radius and of the pressure inside the cocoon. We also suppose that, near the nucleus, the jet propagates in a constant density atmosphere and, as it leaves the central region of the host galaxy, it propagates in a decaying atmosphere. All these assumptions can be used to calculate the evolution of the source radio luminosity allowing us to draw a P-D diagram. This can then be compared with the observed P-D diagram of both compact (GPS and CSS) and extended sources from the 3CR catalogue. The comparison makes it possible to determine the various parameters of the model and understand the physical processes involved in the evolution of extragalactic radio sources.